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chemist pursues his atoms, while the physical investigator
has his own large field in optical, thermal, electrical,
acoustical, and other phenomena. The British Associa-
tion then, as a whole, faces physical Nature on all sides
and pushes knowledge centrifugally outward, the sum of
its labors constituting what Fichte might call the sphere of
natural knowledge. In the meetings of the Association it
is found necessary to resolve this sphere into its component
parts, which take concrete form under the respective letters
of our Sections.

This is the Mathematical and Physical Section. Mathe-
matics and physics have been long accustomed to coalesce.
For, no matter how subtle a natural phenomenon may be,
whether we observe it in the region of sense, or follow it
into that of imagination, it is in the long-run reducible to
mechanical laws. But the mechanical data once guessed
or given, mathematics become all-powerful as an instru-
ment of deduction. The command of geometry over the
relations of space, the far-reaching power which organized
symbolic reasoning confers, are potent both as means of
physical discovery, and of reaping the entire fruits of dis-
covery. Indeed, without mathematics, expressed or im-
plied, our knowledge of physical science would be friable
in the extreme.

Side by side with the mathematical method we have
the method of experiment. Here, from a starting-point
furnished by his own researches, or those of others, the in-
vestigator proceeds by combining intuition and verification.
He ponders the knowledge he possesses and tries to push
it further, he guesses and checks his guess, he conjectures
and confirms or explodes his conjecture. These guesses
and conjectures are by no means leaps in the dark; for
knowledge once gained casts a faint light beyond its own
immediate boundaries. There is no discovery so limited
as not to illuminate something beyond itself. The force

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